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Now gaunt.c seems 100% compatible with original gevero's code. 

Potential problems (would be present in gevero's code as well)
with input m=1, n=19, mu=-10, nu=42, because alphap1 is „old“ before
zAp4d2)


Former-commit-id: adad053fb0022511ff98f78a7094db4e8639b519
This commit is contained in:
Marek Nečada 2017-04-04 04:02:04 +03:00
parent d5bca9f10d
commit e7b7003abd
1 changed files with 129 additions and 96 deletions
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225
qpms/gaunt.c
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@ -3,7 +3,7 @@
#include <stdio.h> #include <stdio.h>
#include <assert.h> #include <assert.h>
#define ZERO_THRESHOLD 1.e-8 #define ZERO_THRESHOLD 1.e-8
#define BF_PREC 1.e-14 #define BF_PREC 1.e-10
// "Besides, the determined Real Programmer can write FORTRAN programs in any language." // "Besides, the determined Real Programmer can write FORTRAN programs in any language."
// -- Ed Post, Real Programmers Don't Use Pascal, 1982. // -- Ed Post, Real Programmers Don't Use Pascal, 1982.
@ -162,32 +162,32 @@ double f_a2normr(int m, int n, int mu, int nu, double a1norm) {
if (!Ap4) { if (!Ap4) {
if(!Ap6) { if(!Ap6) {
double c0=(p+2)*(p1+1)*alphap1; double c0=(p+2.)*(p1+1.)*alphap1;
double c1=(p+1)*(p2+2)*alphap2; double c1=(p+1.)*(p2+2.)*alphap2;
return (c1/c0)*a1norm; return (c1/c0)*a1norm;
} else /* Ap6 != 0 */ { } else /* Ap6 != 0 */ {
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double c0=(p+2)*(p+3)*(p+5)*(p1+1)*(p1+2)*(p1+4)*Ap6*alphap1; double c0=(p+2.)*(p+3.)*(p+5.)*(p1+1.)*(p1+2.)*(p1+4.)*Ap6*alphap1;
double c1=(p+5)*(p1+4)*Ap6*(Ap2*Ap3+(p+1)*(p+3)*(p1+2)*(p2+2)*alphap2); double c1=(p+5.)*(p1+4.)*Ap6*(Ap2*Ap3+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*alphap2);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6+(p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6+(p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
return (c1/c0)*a1norm+(c2/c0); return (c1/c0)*a1norm+(c2/c0);
} }
} else /* Ap4 != 0 */ { } else /* Ap4 != 0 */ {
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
double alphap3=f_alpha(n,nu,p+3); double alphap3=f_alpha(n,nu,p+3);
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2 \ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2 \
+ (p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; + (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
return (c1/c0)*a1norm+(c2/c0); return (c1/c0)*a1norm+(c2/c0);
} }
@ -384,6 +384,7 @@ void gaunt_cz(int m, int n, int mu, int nu, int qmaxa, double *v_aq, int *error)
// FIXME set some sensible return value // FIXME set some sensible return value
void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error) { void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error) {
double alphap1;
*error = 0; *error = 0;
int v_zero[qmax]; int v_zero[qmax];
for (int i = 0; i < qmax; i++) v_zero[i] = 1; for (int i = 0; i < qmax; i++) v_zero[i] = 1;
@ -403,7 +404,7 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
break; break;
case 1: case 1:
v_aq[0] = f_a0(m,n,mu,nu); v_aq[0] = f_a0(m,n,mu,nu);
v_aq[1] = v_aq[0] + f_a1norm(m,n,mu,nu); v_aq[1] = v_aq[0] * f_a1norm(m,n,mu,nu);
// controllo gli zeri // controllo gli zeri
if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) { if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) {
v_aq[1] = 0.; v_aq[1] = 0.;
@ -413,7 +414,7 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
case 2: case 2:
v_aq[0] = f_a0(m,n,mu,nu); v_aq[0] = f_a0(m,n,mu,nu);
v_aq[1] = v_aq[0] + f_a1norm(m,n,mu,nu); v_aq[1] = v_aq[0] * f_a1norm(m,n,mu,nu);
// controllo gli zeri // controllo gli zeri
if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) { if (fabs(v_aq[1]/v_aq[0]) < ZERO_THRESHOLD) {
v_aq[1] = 0.; v_aq[1] = 0.;
@ -613,24 +614,24 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
int p=n+nu-2*(2); int p=n+nu-2*(2);
int p1=p-m-mu; int p1=p-m-mu;
int p2=p+m+mu; int p2=p+m+mu;
double alphap1=f_alpha(n,nu,p+1); alphap1=f_alpha(n,nu,p+1);
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Con questo if decido se mi serve la ricorsione a 3 o 4 termini //Con questo if decido se mi serve la ricorsione a 3 o 4 termini
if (Ap4==0) { //Ap4_2_if if (Ap4==0) { //Ap4_2_if
//Calcolo i restanti valori preliminari //Calcolo i restanti valori preliminari
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
int Ap6=f_Ap(m,n,mu,nu,p+6); double Ap6=f_Ap(m,n,mu,nu,p+6);
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double alphap6=f_alpha(n,nu,p+6); double alphap6=f_alpha(n,nu,p+6);
//Calcolo i coefficienti per la ricorsione ma non c3 perche' qui e solo qui non mi serve //Calcolo i coefficienti per la ricorsione ma non c3 perche' qui e solo qui non mi serve
double c0=(p+2)*(p+3)*(p+5)*(p1+1)*(p1+2)*(p1+4)*Ap6*alphap1; double c0=(p+2.)*(p+3.)*(p+5.)*(p1+1.)*(p1+2.)*(p1+4.)*Ap6*alphap1;
double c1=(p+5)*(p1+4)*Ap6*(Ap2*Ap3 + (p+1)*(p+3)*(p1+2)*(p2+2)*alphap2); double c1=(p+5.)*(p1+4.)*Ap6*(Ap2*Ap3 + (p+1.)*(p+3.)*(p1+2.)*(p2+2.)*alphap2);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6 + (p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6 + (p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
//Calcolo il mio coefficiente //Calcolo il mio coefficiente
v_aq[2]=(c1/c0)*v_aq[1]+(c2/c0)*v_aq[0]; v_aq[2]=(c1/c0)*v_aq[1]+(c2/c0)*v_aq[0];
@ -643,10 +644,10 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
//Calcolo coefficienti ricorsione //Calcolo coefficienti ricorsione
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ \ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+ \
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
//Calcolo il mio coefficiente //Calcolo il mio coefficiente
v_aq[2]=(c1/c0)*v_aq[1]+(c2/c0)*v_aq[0]; v_aq[2]=(c1/c0)*v_aq[1]+(c2/c0)*v_aq[0];
@ -675,26 +676,26 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
int p=n+nu-2*(q); int p=n+nu-2*(q);
int p1=p-m-mu; int p1=p-m-mu;
int p2=p+m+mu; int p2=p+m+mu;
double alphap1=f_alpha(n,nu,p+1); alphap1=f_alpha(n,nu,p+1);
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Con questo if decido se mi serve la ricorsione a 3 o 4 termini //Con questo if decido se mi serve la ricorsione a 3 o 4 termini
if (Ap4==0) { // Ap4_bwd_if: IF (Ap4==0) THEN if (Ap4==0) { // Ap4_bwd_if: IF (Ap4==0) THEN
//Calcolo i restanti valori preliminari //Calcolo i restanti valori preliminari
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
int Ap6=f_Ap(m,n,mu,nu,p+6); double Ap6=f_Ap(m,n,mu,nu,p+6);
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double alphap6=f_alpha(n,nu,p+6); double alphap6=f_alpha(n,nu,p+6);
//Calcolo i coefficienti per la ricorsione ma non c3 perche' qui e solo qui non mi serve //Calcolo i coefficienti per la ricorsione ma non c3 perche' qui e solo qui non mi serve
double c0=(p+2)*(p+3)*(p+5)*(p1+1)*(p1+2)*(p1+4)*Ap6*alphap1; double c0=(p+2.)*(p+3.)*(p+5.)*(p1+1.)*(p1+2.)*(p1+4.)*Ap6*alphap1;
double c1=(p+5)*(p1+4)*Ap6*(Ap2*Ap3 + (p+1)*(p+3)*(p1+2)*(p2+2)*alphap2); double c1=(p+5.)*(p1+4.)*Ap6*(Ap2*Ap3 + (p+1.)*(p+3.)*(p1+2.)*(p2+2.)*alphap2);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6 + (p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6 + (p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
double c3=-(p+2)*(p+4)*(p+5)*(p2+3)*(p2+5)*(p2+6)*Ap2*alphap6; double c3=-(p+2.)*(p+4.)*(p+5.)*(p2+3.)*(p2+5.)*(p2+6.)*Ap2*alphap6;
//Calcolo il mio coefficiente //Calcolo il mio coefficiente
v_aq[q]=(c1/c0)*v_aq[q-1]+(c2/c0)*v_aq[q-2]+(c3/c0)*v_aq[q-3]; v_aq[q]=(c1/c0)*v_aq[q-1]+(c2/c0)*v_aq[q-2]+(c3/c0)*v_aq[q-3];
@ -707,10 +708,10 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
//Calcolo coefficienti ricorsione //Calcolo coefficienti ricorsione
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ \ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+ \
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
//Calcolo il mio coefficiente //Calcolo il mio coefficiente
v_aq[q]=(c1/c0)*v_aq[q-1]+(c2/c0)*v_aq[q-2]; v_aq[q]=(c1/c0)*v_aq[q-1]+(c2/c0)*v_aq[q-2];
@ -765,19 +766,19 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
int p=n+nu-2*(q); int p=n+nu-2*(q);
int p1=p-m-mu; int p1=p-m-mu;
int p2=p+m+mu; int p2=p+m+mu;
double alphap1=f_alpha(n,nu,p+1); alphap1=f_alpha(n,nu,p+1);
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap3=f_alpha(n,nu,p+3); double alphap3=f_alpha(n,nu,p+3);
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Calcolo coefficienti ricorsione //Calcolo coefficienti ricorsione
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
//Ricorsione e residuo //Ricorsione e residuo
aq_fwd=-(c1/c2)*v_aq[q-1]+(c0/c2)*v_aq[q]; aq_fwd=-(c1/c2)*v_aq[q-1]+(c0/c2)*v_aq[q];
@ -833,7 +834,7 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
//$$$$$$$$$$$$$$$$ //$$$$$$$$$$$$$$$$
//Calcolo Ap4 per qi+2 per vedere quale schema usare //Calcolo Ap4 per qi+2 per vedere quale schema usare
int p=n+nu-2*(qi+2); int p=n+nu-2*(qi+2);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Scelgo la ricorrenza a seconda del valore di Ap4 //Scelgo la ricorrenza a seconda del valore di Ap4
if (Ap4==0) { // Ap4_q1_if if (Ap4==0) { // Ap4_q1_if
@ -845,11 +846,11 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
int p2=p+m+mu; int p2=p+m+mu;
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double alphap6=f_alpha(n,nu,p+6); double alphap6=f_alpha(n,nu,p+6);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
int Ap6=f_Ap(m,n,mu,nu,p+6); double Ap6=f_Ap(m,n,mu,nu,p+6);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6 + (p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6 + (p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
double c3=-(p+2)*(p+4)*(p+5)*(p2+3)*(p2+5)*(p2+6)*Ap2*alphap6; double c3=-(p+2.)*(p+4.)*(p+5.)*(p2+3.)*(p2+5.)*(p2+6.)*Ap2*alphap6;
aq_fwd=-(c2/c3)*v_aq[qi+1]; aq_fwd=-(c2/c3)*v_aq[qi+1];
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -901,12 +902,12 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap3=f_alpha(n,nu,p+3); double alphap3=f_alpha(n,nu,p+3);
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
aq_fwd=-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo aq_fwd=-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -937,7 +938,7 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
//Calcolo Ap4 per qi+2 per vedere quale schema usare //Calcolo Ap4 per qi+2 per vedere quale schema usare
int p=n+nu-2*(qi+2); int p=n+nu-2*(qi+2);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Scelgo la ricorrenza a seconda del valore di Ap4 //Scelgo la ricorrenza a seconda del valore di Ap4
if (Ap4==0) { // Ap4_q2_if if (Ap4==0) { // Ap4_q2_if
@ -949,13 +950,13 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double alphap6=f_alpha(n,nu,p+6); double alphap6=f_alpha(n,nu,p+6);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
int Ap6=f_Ap(m,n,mu,nu,p+6); double Ap6=f_Ap(m,n,mu,nu,p+6);
double c1=(p+5)*(p1+4)*Ap6*(Ap2*Ap3 + (p+1)*(p+3)*(p1+2)*(p2+2)*alphap2); double c1=(p+5.)*(p1+4.)*Ap6*(Ap2*Ap3 + (p+1.)*(p+3.)*(p1+2.)*(p2+2.)*alphap2);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6 + (p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6 + (p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
double c3=-(p+2)*(p+4)*(p+5)*(p2+3)*(p2+5)*(p2+6)*Ap2*alphap6; double c3=-(p+2.)*(p+4.)*(p+5.)*(p2+3.)*(p2+5.)*(p2+6.)*Ap2*alphap6;
aq_fwd=-(c1/c3)*v_aq[qi+2] -(c2/c3)*v_aq[qi+1]; aq_fwd=-(c1/c3)*v_aq[qi+2] -(c2/c3)*v_aq[qi+1];
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -1002,13 +1003,13 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap3=f_alpha(n,nu,p+3); double alphap3=f_alpha(n,nu,p+3);
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
aq_fwd=(c0/c2)*v_aq[qi+2]-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo aq_fwd=(c0/c2)*v_aq[qi+2]-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -1035,7 +1036,7 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
//Calcolo Ap4 per qi+2 per vedere quale schema usare //Calcolo Ap4 per qi+2 per vedere quale schema usare
int p=n+nu-2*(qi+2); int p=n+nu-2*(qi+2);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
//Scelgo la ricorrenza a seconda del valore di Ap4 //Scelgo la ricorrenza a seconda del valore di Ap4
if (Ap4==0) { // Ap4_qq_if if (Ap4==0) { // Ap4_qq_if
@ -1048,14 +1049,14 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap5=f_alpha(n,nu,p+5); double alphap5=f_alpha(n,nu,p+5);
double alphap6=f_alpha(n,nu,p+6); double alphap6=f_alpha(n,nu,p+6);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap5=f_Ap(m,n,mu,nu,p+5); double Ap5=f_Ap(m,n,mu,nu,p+5);
int Ap6=f_Ap(m,n,mu,nu,p+6); double Ap6=f_Ap(m,n,mu,nu,p+6);
double c0=(p+2)*(p+3)*(p+5)*(p1+1)*(p1+2)*(p1+4)*Ap6*alphap1; double c0=(p+2.)*(p+3.)*(p+5.)*(p1+1.)*(p1+2.)*(p1+4.)*Ap6*alphap1;
double c1=(p+5)*(p1+4)*Ap6*(Ap2*Ap3 + (p+1)*(p+3)*(p1+2)*(p2+2)*alphap2); double c1=(p+5.)*(p1+4.)*Ap6*(Ap2*Ap3 + (p+1.)*(p+3.)*(p1+2.)*(p2+2.)*alphap2);
double c2=(p+2)*(p2+3)*Ap2*(Ap5*Ap6 + (p+4)*(p+6)*(p1+5)*(p2+5)*alphap5); double c2=(p+2.)*(p2+3.)*Ap2*(Ap5*Ap6 + (p+4.)*(p+6.)*(p1+5.)*(p2+5.)*alphap5);
double c3=-(p+2)*(p+4)*(p+5)*(p2+3)*(p2+5)*(p2+6)*Ap2*alphap6; double c3=-(p+2.)*(p+4.)*(p+5.)*(p2+3.)*(p2+5.)*(p2+6.)*Ap2*alphap6;
aq_fwd=(c0/c3)*v_aq[qi+3]-(c1/c3)*v_aq[qi+2] -(c2/c3)*v_aq[qi+1]; aq_fwd=(c0/c3)*v_aq[qi+3]-(c1/c3)*v_aq[qi+2] -(c2/c3)*v_aq[qi+1];
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -1110,13 +1111,13 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
double alphap2=f_alpha(n,nu,p+2); double alphap2=f_alpha(n,nu,p+2);
double alphap3=f_alpha(n,nu,p+3); double alphap3=f_alpha(n,nu,p+3);
double alphap4=f_alpha(n,nu,p+4); double alphap4=f_alpha(n,nu,p+4);
int Ap2=f_Ap(m,n,mu,nu,p+2); double Ap2=f_Ap(m,n,mu,nu,p+2);
int Ap3=f_Ap(m,n,mu,nu,p+3); double Ap3=f_Ap(m,n,mu,nu,p+3);
int Ap4=f_Ap(m,n,mu,nu,p+4); double Ap4=f_Ap(m,n,mu,nu,p+4);
double c0=(p+2)*(p+3)*(p1+1)*(p1+2)*Ap4*alphap1; double c0=(p+2.)*(p+3.)*(p1+1.)*(p1+2.)*Ap4*alphap1;
double c1=Ap2*Ap3*Ap4+(p+1)*(p+3)*(p1+2)*(p2+2)*Ap4*alphap2+ double c1=Ap2*Ap3*Ap4+(p+1.)*(p+3.)*(p1+2.)*(p2+2.)*Ap4*alphap2+
(p+2)*(p+4)*(p1+3)*(p2+3)*Ap2*alphap3; (p+2.)*(p+4.)*(p1+3.)*(p2+3.)*Ap2*alphap3;
double c2=-(p+2)*(p+3)*(p2+3)*(p2+4)*Ap2*alphap4; double c2=-(p+2.)*(p+3.)*(p2+3.)*(p2+4.)*Ap2*alphap4;
aq_fwd=(c0/c2)*v_aq[qi+2]-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo aq_fwd=(c0/c2)*v_aq[qi+2]-(c1/c2)*v_aq[qi+1]; //E' qui che lo calcolo
//A seconda che il mio valore sia 0 o meno confronto i valori //A seconda che il mio valore sia 0 o meno confronto i valori
@ -1166,6 +1167,38 @@ void gaunt_xu(int m, int n, int mu, int nu, int qmax, double *v_aq, int *error)
} // qmax_case } // qmax_case
} // gaunt_xu } // gaunt_xu
#ifdef GAUNTTEST
#define MIN(x,y) (((x) > (y)) ? (y) : (x))
static inline int q_max(int m, int n, int mu, int nu) {
return MIN(n, MIN(nu,(n+nu-abs(m+mu))/2));
}
void __vec_trans_MOD_gaunt_xu(const double *m, const double *n, const double *mu, const double *nu, const int *qmax, double *v_aq, int *err);
int main()
{
int NMAX=20, REPEAT=10;
//int scanned;
int m, n, mu, nu;
for (int r = 0; r < REPEAT; ++r) for (n = 1; n < NMAX; ++n) for (nu = 1 ; nu < NMAX; ++nu)
for (mu = -nu; mu <=nu; ++mu) for (m = -n; m <= n; ++m) {
//while(EOF != (scanned = scanf("%d %d %d %d", &m, &n, &mu, &nu))) {
// if (scanned != 4) continue;
// printf("%d %d %d %d\n", m, n, mu, nu);
double mf = m, nf = n, muf = mu, nuf = nu;
int qmax = q_max(m,n,mu,nu);
double v_aq_c[qmax+1], v_aq_f[qmax+1];
int errc, errf;
__vec_trans_MOD_gaunt_xu(&mf, &nf, &muf, &nuf, &qmax, v_aq_f, &errf);
gaunt_xu(m,n,mu,nu,qmax,v_aq_c, &errc);
// for(int i = 0; i <= qmax; ++i) printf("%f ", v_aq_c[i]);
// puts("(c)");
// for(int i = 0; i <= qmax; ++i) printf("%f ", v_aq_f[i]);
// puts("(f)");
// for(int i = 0; i <= qmax; ++i) printf("%e ", v_aq_f[i] - v_aq_c[i]);
// puts("(f-c)");
}
return 0;
}
#endif //GAUNTTEST